Help finding an exponential equation...

It starts out as a straight line in stage one
In stage two, I kind of tents up...

Stage zero________ Notice it is all one segment
Stage Two____/\______ This is now Four segments
Then, both sides of that tent tent up too.

So first I have to make a table of the first few stages...

Stage |* |0 |1 |2 |3 |4 |
segments|1 |4 |16|40|88|

And now I have to find the equation, but I don't seem to get it enough to do that.... But I think I should know how to find the equation from points by now,
So I'm asking two questions really...
A: What is the equation
B Why?
Thanks for the urgent help. THis is due tomorrow (!)

It starts out as a straight line in stage one
In stage two, I kind of tents up...

Stage zero________
Stage Two____/\______
Then, both sides of that tent tent up too.

So first I have to make a table of the first few stages...

Stage |0 |1 |2 |3 |4 |
segments|1 |4 |16|40|88|

And now I have to find the equation, but I don't seem to get it enough to do that.... But I think I should know how to find the equation from points by now,
So I'm asking two questions really...
A: What is the equation
B Why?
Thanks for the urgent help. THis is due tomorrow (!)